# Why do we always choose centre-of-mass frame to study particle physics problems (e.g. Feynman diagrams)? Even in non-relativistic regimes (v<0.3c)

Example: electron positron annihilation forbids a single photon production, and searching through this forum (Why can't a single photon produce an electron-positron pair?) and a few books, they always reason with this by using the centre of mass frame of reference where the two incoming bodies $$e^{+}$$ and $$e^{-}$$ have equal and opposite momentum, hence due to conservation of energy and momentum the final state (photon) cannot exist since a photon with no momentum is impossible.

However considering a frame of reference - stationary - at the point of collision of an electron and a positron incoming at a 90 degree angle to each other, what forbids a single photon production?

• Well, it is not only a convenient frame to do things in (even for classical mechanics), plus you separate out the interaction problem from the what-you-see-in-the-lab problem. (And, 0.3c is pretty relativistic). – Jon Custer Mar 21 at 17:40
• I am not sure about this, the low end of mildly relativistic cases is b>0.3. For b<0.3 the γ is generally approximated as ~1. – Gav Chatz Mar 25 at 11:22